(Finitely) subdirectly irreducibles and Birkhoff-like sheaf representation for certain varieties of lattice ordered structures

Global subdirect products of mutually disjoint algebras are exactly the algebras of global sections of sheaves [17]. We say that an algebra A is globally indecomposable if for every global subdirect product A1¤ {Ai : i I} such that A1 is isomorphic to A and I is a compact space we have that there exists i I such that pi : A1“Ai is an isomorphism, where pi is the canonical projection. For an algebra A, Con(A) denotes the congruence lattice of A and for a class M of algebras define S(A, M)= {u Con(A): A/u$B for some B in M}. In this paper we search the varieties of